4- A sinusodial wave is traveling on a string with speed 40 m/s. The displacemen

Question

4- A sinusodial wave is traveling on a string with speed 40 m/s. The displacement of the particles of the string at x = 10 cm varies with time according to y = (5.0 cm) sin [ 1.0 - (4.0 s-1)t]. The linear density of the string is 4.0 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form y(x, t) =sin(kx plus-minus italic omega t), what are (c) ym, (d)k, (e) italic omega , and (f) the correct choice of sign in front of italic omega ? (g) What is the tension in the string?

Explanation / Answer

a] frequency = angular frequency / 2 pi = 0.63 Hz

b]wavelength = 2pi/K = 6.28 m

c]y = the position in the y direction of the particle

d]K = the spring constant of the rope

e]italic omega = angular frequency

f] the correct choice of sign in front of omega is the direction of the wave

g] tension

v = sqrt [T/rho]

= 40^2 = T / rho

= T = 640 N

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